Charges for 10 seconds and stops - battery cycle?

Today I saw very strange behavior. Started the car and drove 9-10 miles with 45mph on cruise control, then about a mile downhill and then stopped at traffic light. The battery was 1 bar to full, but the ICE started and kept running. After few more miles, when arrived, I didn't turn of the car and watched the strange behavior:
10 seconds charging; 10 seconds not charging and this keep repeating for around 20-30 minutes. While charging, the engine was running rough with little vibrations, and when moving from charging/not charging state the car (was in P) moved a bit forward and back. The last 2-3 charging cycles was longer, for about a minute then the ICE stopped. After that everything was back to normal and I took the same route to home without anything abnormal.

Is it some kind of a battery cycle or indicates a problem?

 

Thank you, Bisco!
It has 104k miles, when I stopped, the SOC was around 50%. When charging 1 bar was added, when discharging - 1 bar down. After those 20-30 minutes the SOC level was varying as usual.

 

No, I'm the second owner, bought it about 4 months and 10k miles ago. But the mileage is genuine and nobody messed with the odo. The car has full service history in Toyota and the only strange thing in it was that when it was ~55k mies old, Toyota performed (or couldn't perform...) some kind of software update that f*cked the inverter and it was changed under warranty.
The 12v battery is new - changed it before ~1000 miles, but it's regular lead-acid 44Ah battery, not AGM type. Maybe it's connected to another problem that I posted today: Prius 2011 - P0A7F | PriusChat.
Maybe I should wrote in that topic, sorry.

 

I've connected the ventilation hose that takes those gases out. I've owned a Volvo which battery was in the same location and was also lead-acid, but it had two of those pipes for each side of the battery. The battery I bought came with a plug to be put in the opposite side of the ventilation hose ("unused" side). Not sure, but as far as I know, the OEM battery of the Prius 3 in Europe is lead-acid too.

 

Thank you for the reply, David! The new battery is not a problem, but I want to be sure if I'll purchase a new one. Is it possible to be some kind of a software or module issue and not with the battery?
I wrote to a seller in alibaba!com, representing cebabattery!com and he told me that they manufacture Prius 3 battery packs and sell them for $1000 and the shipping to the EU is $355 which I think is a good price. Strange thing is that their batteries are not rectangular, but cylindrical. Does anyone have experience with those Chinese batteries, are they a crappy product? The guy sent me this video about the battery pack installation, where the cylindrical batteries can be seen:

I haven't asked my local Toyota dealer for prices yet, but as far as I know their rates, it would cost much more than the prices you quoted.

 

Thank you both for the answers and help! I'll look up for some info about the battery recharging/reconditioning and then will write to Jeff.
Tomorrow I'll check the local Toyota dealer for prices on new battery and if they offer rebuilt ones. Prices here are a bit different than in the US, e.g. the new Prius starts at about $34k, the 2.3 Mustang starts at $57k But definitely a battery from Toyota would be a better choice. I think not to rush and wait until it dies completely or I start to get lower mpg (now it's ~56 on the highway with cruise control at 70 mph and ~49 at the city with a lot of traffic and traffic lights. Tires are not most efficient ones - 17" Pirelli P Zero Nero). Definitely won't scrap the car, because it's in good condition, fresh interior and has good equipment.

Today decided to check the copper battery connectors for corrosion and they weren't in very good shape. Disassembled everything and cleaned them. I don't think the cleaning will make any difference, but decided to try. Took the opportunity to measure the individual modules (without a load, for example 12v headlight bulb) and the middle ones were little undervolted - 7.30v, the side ones were 7.4 - 7.5v. I'm attaching some photos of how the copper plates looked.

PS: When connected all the wiring and went to test if the car starts ok, I almost shаt myself when it didn't go into the "READY" mode and the yellow triangle appeared. Turned out I forgot to lock the safety plug...

 

Here are the prices from Toyota at my country:
New battery (only the battery modules, without the relays, modules, cooling fan, etc): $5500
New battery if the old one is returned: $4280
Toyota does not offer rebuilt ones, and they don't have a charger to cycle the battery cells with discharge-charge cycles. Only to charge the battery if the car does not start.
As I thought - I'm crossing out our local Toyota dealer from the options when this have to be fixed.

 

Update about the situation...
Last months I was driving another cars and did little driving with the Prius - about 3'100 miles (5'000 km) after the cleaning, the "Check hybrid system" message appeared again.

This time the error was P0A80 Went out and after 6-7 miles the error lit up. Cleared it using the Wi-Fi elm and did 320 miles trip without any issues. I'm going home after few days and new 320 miles and I'll check the individual modules with load using a 55w headlight bulb. I'll report back when I check them.
I think it will need 4-5 modules judging by the Hybrid Assistant app.